It doesn’t matter how many years you have been a successful chef or what famous culinary school you went to, whatever you think the important differences between stock and broth are, there will surely be others with similarly impressive credentials as you, who have different opinions.
There is a difference, but I think it’s more of a spectrum than a black or white issue. Some say that stocks are merely simmered bones with no seasoning, vegetables or other ingredients involved, while broth is boiled meat with vegetables and sometimes spices and seasoning added to the mix. Others say that both broth and stock can contain bones as well as meat, but the important difference is the ratio of meat to bone, whereas a stock would contain more bone and visa versa. Another opinion is that broths are merely flavoured stocks. Still others say broth is stock that is being used in a soup. Salt content is sometimes described as being the critical difference as well. Sifting through the intricacies of the arguments can become quite tedious.
If forced to ultimately distinguish between the two I would say that they are the same, save that stocks are made with bones and broths are made with meat. Stocks are thick and gelatinous like jello when cooled because of the collagen that is extracted from the bones and connective tissues while simmering. The gelatinous quality of stock makes it better than broth for deglazing pans and is often used in place of butter or cream to make sauces in this way. Pure broth will stay liquid when cooled and will not taste quite as rich as a stock. This can be a desirable quality for light soups and other recipes that require a lighter flavour. It seems that many people feel that stocks should not include vegetables, but I don’t see any reason why they should not. I feel that if the dish you are preparing cannot do with the subtle flavours that vegetable add to a stock than one can merely make a stock without vegetables. To this Ill add that while vegetables seem to usually be required for a broth, there is no law against making a simple broth with only meat. When I make chicken broth I usually use bones and meat and the result is gelatinous when refrigerated, so I suppose that could be considered a stock, but I also put vegetables into it and use it as a base for soups, sometimes with water added to thin it if it is meant to be a light soup. The important thing, I think, is to use what is best for the recipe and call it what you like, whether it falls directly into the pure definition of the word or not.
To summarize, in my non-expert opinion stock and broth can be considered the same thing. You may choose to make a gelatinous broth by using bones or meat and bone combination or you can use only meat for a lighter result. Either way it will be delicious and will certainly out do anything you can buy at the store. You can detect the simplicity and taste the freshness in a homemade broth. I strongly urge you to try making it if you never have before. It takes time, but it is very little work. (recipe for chicken stock HERE)